Nonlinear Magnetic Circuit Research Articles

Application of the modified approach of Finite Element Method for determining the displacement current distribution in nonlinear magnetic circuits

Application of the modified approach of Finite Element Method for determining the displacement current distribution in nonlinear magnetic circuits

Structure optimization design and magneto-mechanical characteristics analysis of amorphous alloy with oriented silicon steel composite wound core

Three-dimensional wound cores are widely used in three-phase distribution transformer due to the symmetrical magnetic circuit structure. Amorphous alloy and oriented silicon steel are two kinds of ferromagnetic materials commonly used to make distribution transformer cores, each has own advantages and disadvantages in magnetic and mechanical characteristics. The amorphous alloy and oriented silicon steel composite core can synthesize the advantages of both. In this paper, a double-layer composite wound core (DCWC) structure is proposed and the corresponding dual nonlinear electric circuit and magnetic circuit coupling model is established. A structure optimization design method for the DCWC based on the free parameter scanning method is proposed by taking the percentage of oriented silicon steel in the composite core and the structure parameters as free variables. Based on the proposed optimization design method, a DCWC is designed and the experimental prototypes are manufactured. Further, the flux density distribution, core loss and mechanical vibration displacement of the DCWC are analyzed, and the effectiveness of the proposed method is verified by comparing with the measured results.

A 3D nonlinear magnetic equivalent circuit model for an axial field flux focusing magnetic gear: Comparison of fixed-point and Newton–Raphson methods

An axial field flux focusing magnetic gear is being modeled in this study utilizing a 3D magnetic equivalent circuit technique that takes into consideration the magnetic saturation of the soft magnetic material. Considering magnetic saturation is a critical feature in modeling magnetic gears, particularly those with flux focusing arrangements where specific regions become highly saturated. However, nonlinear modeling comes with its costs, like increased computation time and resource allocation, so it has always been a hot topic for research and development. The implementation of two nonlinear iterative solvers for the solution of the nonlinear magnetic equivalent circuit was described and a comparison between the two methods was done. The approach presented was chosen to be a good lightweight alternative for 3D finite element method modeling that can be used for early design stages. It provided acceptable nonlinear predictions while requiring less time than a 3D finite element method model and saving memory and resources.

Multiparameter Identification for Active Magnetic Bearing With Uncertainties Based on a Coupled Nonlinear Model

Parameter identification enables active magnetic bearing (AMB) to obtain more state information, which can be used for control optimization, condition monitoring and fault diagnosis for rotating machinery. Due to the limitation of working principle and modeling accuracy, the traditional parameter identification methods show inherent disadvantages in cost, applicability or precision. Thus, this paper proposes an accurate multi-parameter identification method without any instrumentation. This method takes into account the electromagnetic force coupling caused by the asymmetric magnetic circuit, the non-linearity caused by the saturation effect, together with the uncertain parameters caused by machining and assembly errors, temperature, etc. Firstly, the coupled nonlinear magnetic circuit model of the AMB is established by the reluctance network method, and the influence of non-ideal factors on the electromagnetic force is treated. Secondly, a novel experimental method for parameter identification is presented. According to the equilibrium relationship between the electromagnetic force and the supporting load, the force balance equations of the rotor under different working conditions are obtained. Taking the supporting parameters and uncertain geometric parameters as the parameters to be identified, the multi-parameter identification model is established. Finally, the proposed method is validated by the finite element method (FEM) and experiments. The results show that the method can accurately identify the air gap length, rotor origin, static supporting load, and stiffness of the AMB.

Analysis and Compensation of Hysteresis Effect on Electromagnetic Force in Axial Magnetic Bearings

Magnetic bearings (MBs) enable the rotor to run at high speed without lubrication due to no mechanical contact. However, the inherent hysteresis of ferromagnetic materials affects the support characteristics, reducing the design performance and stability margin of MBs, especially for axial MBs using materials with high coercive force. To analyze and compensate for the hysteresis effect on the electromagnetic force in axial MBs, an efficient method is proposed in this paper. Firstly, the hysteresis properties of the ferromagnetic materials are simulated by the Preisach model, and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> relationships under any external magnetic field can be determined. Taking into account the non-ideal factors such as hysteresis and saturation effects, the nonlinear magnetic circuit model of the axial MBs is established. The magnetic flux density working point under different control currents and eccentric displacements can be determined through iterative calculation, and then the air gap flux density distribution and electromagnetic force of the axial MBs are calculated. On this basis, the adverse effects of hysteresis on the bearing capacity and system stability of axial MBs are analyzed. A compensation algorithm is designed based on the inverse model to reduce the hysteresis effect. The inverse model is approximated modeled by the Lissajous curve. Finally, the proposed analysis and control methods are verified by the finite element method (FEM) or experiments. The results show that the proposed analysis method is capable of accomplishing good accuracy and requires less computation time than FEM, it can be applied to arbitrary current variation processes. In addition, the phase lag of the system is effectively improved with the compensation algorithm.

An Electromagnetic Design of Slotless Variable Reluctance PM-Resolver

This paper proposes a novel design of the variable reluctance permanent magnet (VRPM) resolvers. It utilizes a slotless stator to reduce the resolver volume. The proposed design overcomes the complex structure of windings by replacing them with magnetic flux measurement units (MFMU). The new design eliminates the computationally-expensive demodulation process of output signals by relying on none-modulated signals. An analytical model based on the nonlinear magnetic equivalent circuit (MEC) method is used to extract the output signals of the proposed resolver design. The accuracy of applied analytical model is verified against the time-stepping finite-element method (TSFEM). An optimization is implemented to best improve the resolver performance by saturating the stator ribs targeting a minimum possible PM volume. The design aims high flux density of iron to make the resolver robust against external distortions, but at the same time, the flux density of core is kept within the linear region of the B-H curve to avoid saturation. TSFEM is used to further analyze the performance of the optimal slotless VRPM-Resolver in details. The simulation results are verified by experimental tests on a prototyped resolver design.

Modeling and Optimal Design of Inductor-Integrated Three-Phase 3-D Wound Core Transformer Under SPWM Excitation

Compared with the laminated core transformer (LCT), the 3D wound core transformer(3D-WCT) has the characteristics of symmetrical magnetic circuit and low vibration. This article focuses on the modeling and optimal design of the 3D-WCT for isolated DC/AC application. Firstly, based on the Jiles-Aterton model, a nonlinear magnetic circuit model of the 3D-WCT is established to calculate the flux density and core loss accurately under SPWM excitation. A thermal network model is presented for the steady-state temperature-rise calculation of the forced-air cooled 3D-WCT. Secondly, the optimal design method is carried out on the basis of the magnetic circuit and thermal network models. Based on the optimized design results, a regression analysis is performed to establish the relationship between the design variables and the performance objectives. Finally, a 75kVA 3D-WCT prototype is manufactured and tested in the actual inverter power supply to verify the established magnetic circuit and thermal network models. The 3D-WCT prototype is applied to the 150kVA inverter power supply, which contributes to achieving high power density and high efficiency of the power supply.

Hybrid-Magnet Variable Flux Memory Machine With Improved Field Regulation Capability for Electric Vehicle Applications

This article aims to investigate a novel hybrid-magnet variable flux memory machine (VFMM) with improved field regulation capability for electric vehicle applications. Two sets of permanent magnets (PMs), i.e., high-energy-density neodymium–iron–boron PM and low coercive force (LCF) PM, are arranged in a delta array to improve field regulation capability and torque density. The machine topology, key features, and operating principle of the presented machine are demonstrated. Based on the simplified magnetic circuit model, the underlying design tradeoffs of the presented machine are revealed qualitatively. The nonlinear magnetic circuit model of the presented machine taking saturation and hybrid-magnet leakage flux into consideration is built for machine analysis. Electromagnetic performance comparisons are carried out by finite element analysis between the presented VFMM and the existing VFMM. The results show that the presented machine can achieve significantly improved flux regulation capability while maintaining the high output torque due to the improved arrangement of hybrid magnetic branches and enhanced flux concentration effect. Finally, the investigated VFMM is prototyped. The operating principle and predicted results are verified by experimental results.

Non-linear analytical model for synchronous reluctance machine

This paper proposes an non-linear magnetic equivalent circuit (MEC) method for the synchronous reluctance machine (SynRM). The rotor geometry of the prototype machine is not simplified. In addition, the proposed MEC model can be used with different slot/pole combination or dimensions. While modeling SynRM, the non-linear effect and the leakage flux of the windings is taken into account. Due to the non-linear effect of the BH-curve, iterative algorithm process is used to find electromagnetic performances and magnetic permeability of non-linear reluctances. Finally, the proposed MEC is validated by both the finite element method (FEM) and experimental results to prove its accuracy and practicality.

Numerical Study on Unbalance Response of Dual-Rotor System Based on Nonlinear Bearing Characteristics of Active Magnetic Bearings

The magnetic suspended dual-rotor system (MSDS) has the advantage of a high power density. The system can be used in high-speed rotating machinery. The major purpose of this study is to predict the unbalance response of the MSDS considering the nonlinear bearing characteristics of active magnetic bearings (AMBs). Firstly, the nonlinear bearing model was established by a non-linear magnetic circuit method (NMCM). The model considers magnetic flux leakage, magnetic saturation, and working position flotation accurately. Then, the dynamic model of the system was established by using the finite element method and solved by the Newmark-β method. Finally, the effects of external load, rotational speeds, and control parameters were studied. Axial trajectory diagrams, stability zone diagrams, and waterfall diagrams were employed to analyze the dynamic behaviors of the MSDS. The results indicate that the external load, rotational speeds, and control parameters have a significant impact on the unbalance response of the system. Super harmonics of rotational frequencies and their combined frequencies may be excited by heavy load conditions. Appropriate control parameters can suppress the nonlinear phenomena. The obtained results of this research will contribute to the design and fault diagnosis of MSDSs.

A Study on Design Method of Synchronous Reluctance Motor Based on Nonlinear MEC Using Newton-Raphson Method

Recently, policies for carbon reduction are being implemented worldwide to solve environmental and energy consumption problems. Minimum Energy Performance Standard (MEPS) is a carbon reduction policy for reducing energy consumption by regulating the efficiency of industrial induction motors. The induction motors have a low manufacturing cost and a simple structure, and it can be operated without control and have great advantages in maintenance so it is applied in various industrial fields. However, compared with other types of motors, there is a limit to improving the efficiency due to the additional loss generated in the cage of rotor. Synchronous reluctance motors (SynRMs) are attracting the most attention as an alternative to an induction motor since they are composed of only a copper winding and a core, manufacturing cost and durability are excellent Moreover, unlike induction motors, there is no secondary loss; therefore, it is evaluated as a high-efficiency industrial motor corresponding to MEPS. However, because of their complex rotor shape composed of multiple barriers and segments, SynRMs are typically designed using finite-element analysis, requiring a significant amount of time and trial and error. In this paper, a basic design method for a synchronous reluctance motor based on a nonlinear magnetic equivalent circuit using the Newton-Rapson method is presented. Finally, the design method of the synchronous reluctance motor is validated through performance tests using a prototype.

A General Decentralized Dynamic State Estimation With Synchronous Generator Magnetic Saturation

The saturation of the nonlinear magnetic circuit of synchronous generators is often neglected when performing Kalman filter-based dynamic state estimation (DSE), yielding significant estimation bias. This letter addresses this problem and proposes a generalized DSE framework to handle magnetic saturation. Moreover, this letter derives a state initialization procedure that improves the Kalman filter tracking speed. The framework is flexible in dealing with different saturation functions and generator models. Numerical results on the Texas 2000-bus system verify the effectiveness of the proposed method.

Choice of control function in magnetically-coupled full bridge DC-DC power controller for arc welding: A Practical Approach

In a full bridge DC-DC converter (FBDC) the transformer is a major component for controlled power delivery to secondary side isolated DC loads. Its excitation characteristics is nonlinear and it suffers from a serious problem called magnetic saturation. The power loss in it and also in power switching devices connected at its primary are calculated based on the assumption that the DC flux in core is considered zero. Inverter topology often influences the parametric design of transformer. This article elaborates, with detailed practical validation, that the transformer could influence on choice of suitable control function and its gain values. For that, two popular control functions i.e., proportional plus integral (PI) and second order sliding mode control (SOSMC) would be elaborated here. The approach of controller design for PI and SOSMC is different. Collective approach of gain selection in PI results conservative values of its two gains. On the other hand, two gains in SOSMC are purely based on worst-case process behavior, value of each gain is large. For compatibility study of both control functions in FBDC, nonlinear, extremely dynamic, wide range and diverse arc welding process would be considered as load. Experimental results suggests that SOSMC generates superior control performance in terms of robustness features and control response. Still, as this article further establishes with requisite practical validations, that non-linear magnetic circuit could act as a hindrance for effective utilization of capacity of FBDC based on high-gain fractional order SOSMC function.

Nonlinear magnetic circuit – self inductance definitions, passivity and waveforms distortion

Nonlinear magnetic circuit – self inductance definitions, passivity and waveforms distortion

Magnetic Equivalent Circuit and Optimization Method of a Synchronous Reluctance Motor with Concentrated Windings

In this paper, the 12-slot/4-pole (12/4) synchronous reluctance motor (SynRM) with concentrated windings is proposed for low-cost hybrid vehicles. The non-linear magnetic equivalent circuit (MEC) model of the 12/4 SynRM is built to obtain the main electromagnetic characteristics such as coil flux, inductances, torque, etc. The magnetic saturation is also counted in by the MEC. Results calculated by MEC are validated by 2D finite element analysis (FEA). Then, aiming at larger average torque, lower torque ripple and lower total harmonic distortion (THD) in phase voltage, the parameter optimization method of the SynRM is proposed based on the Taguchi method and the MEC model. The proposed Taguchi-MEC method enables a fast optimization with satisfactory accuracy. Finally, the motor prototype is manufactured, and experimental validations are carried out.

Optimal force control of a permanent magnet linear synchronous motor based on a magnetic equivalent circuit model

This paper is concerned with the high dynamic and energy efficient operation of permanent magnet linear synchronous motors (PMLSM). In particular, a novel optimal force control strategy is developed and experimentally validated on a test bench. The proposed control concept is based on a detailed nonlinear magnetic equivalent circuit (MEC) model which, in contrast to classical dq-models, is able to systematically capture nonlinear magnetic saturation effects and non-harmonic motor quantities. The core of the control strategy is an optimization problem which calculates optimal currents and flux linkages such that the desired forces are accurately tracked and, at the same time, the ohmic losses in the coils are minimized. The control strategy comprises a flatness-based feedforward controller and a nonlinear PI-type feedback controller. Experimental results on a test bench confirm that the proposed control concept improves both the control accuracy and the energy efficiency and outperforms state-of-the-art field-oriented control concepts based on the dq-model.

An Efficient Modeling of Air Gap and Nonlinear Analysis of Magnetic Equivalent Circuit for Large Turbogenerators Under No-Load Condition

Fast and accurate modeling of large turbogenerators is of great importance for optimal design and commercial value. Therefore, a 2-D nonlinear magnetic equivalent circuit (MEC) model considering saturation and rotor motion is proposed in this article. When the node-based MEC adopts relaxation iteration for nonlinear calculation, it is not easy to converge by using traditional interpolation function and piecewise fitting of the core <i>B&#x2013;H</i> or <inline-formula> <tex-math notation="LaTeX">$u_{r} (B)$ </tex-math></inline-formula> curve. The main contribution of this article is to find that using continuous fitting function is of great significance for the convergence of nonlinear iteration. At the same time, a simple and effective MEC of air gap is also provided. The flux density of air gap and stator tooth obtained by the proposed method is in good agreement with results of the finite element. No-load characteristics were also verified by the finite element and experiment. The calculation time of a cycle takes about 700 s by the finite element, and however, MEC only takes about 2 s.

Improved magnetic equivalent circuit for dual stator consequent pole permanent magnet machine

This paper proposes a non-linear magnetic equivalent circuit (MEC) model for three different dual stator consequent pole permanent magnet (DSCP-PM) machines. It also includes both no-load and on-load electromagnetic performance criteria. The fundamental of the MEC model is that it takes into the influence of winding flux leakage and iron saturation consideration. Besides, winding magneto motive forces (MMF) of DSCP-PM machines are applied to model both distributed winding and concentrated winding. An iterative algorithm is applied to resolve the problem when magnetic steel is severely saturated. Furthermore, the modeling for DSCP-PM machine provides a standard for modeling this machine. Finally, the MEC model's accuracy and practicality for DSCP-PM machine are validated by the finite element (FE) method.

Torque Ripple Minimization Control Strategy in Synchronous Reluctance Machines

Torque smoothness is an essential requirement for high-performance motor drive applications. Synchronous reluctance machines (SyRM) have high torque ripple due to non-linear magnetic circuit and saturation. Typically, in Permanent magnet machines the active torque ripple compensation is achieved by injecting a compensating ripple current in the <i>q-axis</i>. For SyRM, the current injection method for active torque ripple cancellation can be used in both the <i>d-axis</i> and <i>q-axis</i>. However, the saturation of the motor parameters with the changing current can result in varied performance between the two methods. This paper evaluates the effectiveness of both of these methods for torque ripple cancellation. For evaluation, the impact of parameter saturation with ripple current injection on the <i>d-axis</i> and the <i>q-axis</i> is studied. The mathematical conclusions obtained are evaluated by both the simulation and the experimental results performed on a 4 pole 1200W Synchronous reluctance machine.

Implementation of the sliding-line technique in a MEC model of a linear bistable actuator

PurposeThe aim of this study is to investigate the implementation of the sliding-line technique (SLT) in a generic two-dimensional (2D) nonlinear adaptive magnetic equivalent circuit (MEC) model predicting the electromagnetic force evolution of a linear bistable electromagnetic actuator technology.Design/methodology/approachThe developed MEC model considers the saturation effect and the auto-adjustability of the spatial discretisation. The connection between static and mobile zones is ensured by an approach known as “air-gap sliding-line technique”, which is widely used for rotary electric motor models. To the best of the author’s knowledge, that is the first time that the SLT is implemented on an electromagnetic structure with linear motion.FindingsIt was found that, in case of a linear actuator with a relatively small working stroke, the implementation of the SLT could lead to some non-negligible inaccuracies.Originality/valueTo solve the above-mentioned problem, it was proposed to investigate the implementation of a single SLT vs double SLT. The results of the MEC models were compared with the 2D finite-element analysis (FEA) as well as with the experimental test results. The developed semi-analytical models can be easily adapted to other topologies of linear electromagnetic machines.